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Chapter 31: Q82P (page 940)

A $1.50 mH$ inductor in an oscillatingLCcircuit stores a maxi- mum energy of $10.0 渭 J$ . What is the maximum current?

Short Answer

Expert verified

The maximum current is $0.115 A$ .

Step by step solution

01

Step 1: Given

$U_{\max} = 100 渭闯 = 10 脳 10^{- 6} J$

$L = 1.5 mH = 1.5 脳 10^{- 3} H$

02

Determining the concept

By using the formula for maximum energy in the $LC$ circuit and substituting the given values, find the maximum current.

Formulae are as follows:

$U_{\max} = \frac{1}{2} {LI}^{2}$

Where,

U = magnetic energy.

L = inductance of solenoid.

I = current.

03

Determining the maximum current

$U_{\max} = \frac{1}{2} {LI}^{2}$

Rearranging the terms,

$I^{2} = \frac{2 U_{\max}}{L} I = \sqrt{\frac{2 U_{\max}}{L}} I = \sqrt{\frac{2 脳 10 脳 10^{- 6}}{1.5 脳 10^{- 3}}} I = 0.005 A$

Hence,the maximum current is $0.005 A$ .

Using the formula for maximum energy stored in the LC circuit, found the maximum current in the circuit.

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Most popular questions from this chapter

An RLC circuit such as that of Fig. 31-7 has $R = 5.0 惟$ , $C = 20.0 渭贵$ , $L = 1.0 H$ , and $蔚_{m} = 30.0 V$ . (a) At what angular frequency $蝇_{d}$ will the current amplitude have its maximum value, as in the resonance curves of Fig. 31-16? (b) What is this maximum value? At what (c) lower angular frequency $蝇_{d 1}$ and (d) higher angular frequency $蝇_{d 2}$ will the current amplitude be half this maximum value? (e) For the resonance curve for this circuit, what is the fractional half-width $(蝇_{d 2} - 蝇_{d 1}) / 蝇$ ?

LCoscillators have been used in circuits connected to loudspeakers to create some of the sounds of electronic music. What inductance must be used with a 6.7 碌F capacitor to produce a frequency of10 kHz, which is near the middle of the audible range of frequencies?

In Fig. 31-35, let the rectangular box on the left represent the (high-impedance) output of an audio amplifier, with $r = 1000 ohm$ . Let $R = 10 ohm$ represent the (low-impedance) coil of a loudspeaker. For maximum transfer of energy to the load $R$ we must have $R = r$ , and that is not true in this case. However, a transformer can be used to 鈥渢ransform鈥� resistances, making them behave electrically as if they were larger or smaller than they actually are. (a) Sketch the primary and secondary coils of a transformer that can be introduced between the amplifier and the speaker in Fig. 31-35 to match the impedances. (b) What must be the turns ratio?

An ac voltmeter with a large impedance is connected in turn across the inductor, the capacitor, and the resistor in a series circuit having an alternating emf of $100 V$ (RMS); the meter gives the same reading in volts in each case. What is this reading?

An LC circuit oscillates at a frequency of $10.4 kHz$ . (a) If the capacitance is $340 渭贵$ , what is the inductance? (b) If the maximum current is $7.20 mA$ , what is the total energy in the circuit? (c) What is the maximum charge on the capacitor?

See all solutions

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